Multiplicative Lie Algebra Structures on the Semi-Direct Product of Groups

Key Points

• The study aims to develop a method for identifying multiplicative Lie algebra structures on the semi-direct product of groups under specific conditions.
• Introduced a systematic approach to classify multiplicative Lie algebra structures.
• Analyzed the conditions required for the semi-direct product of groups.
• Investigated the interdependence of multiplicative structures on individual groups.
• Established that every multiplicative Lie algebra structure on the semi-direct product relies on the structures of the individual groups.
• Numerous examples illustrate the application of the method in practice.